Revisiting dissipative motion of a spinning heavy symmetric top and the rise of the top by friction
Keywords:Heavy symmetric top; rise of the top; Jellet’s model; pure slipping model
The dissipative motion and the rise of a heavy symmetrical top with a hemispherical peg are studied. A model taking the fixed point of the top as the center of the peg is considered when the top completely slips and the rolling motion is ignored. This is different from existing models like Jellet's one. Jellett's model and pure slipping are compared for different tops for the rise of the top, and an experimental method to determine the better model is proposed.
V. Tanrıverdi, Dissipative motion of a spinning heavy symmetric top, Eur. J. Phys. 41 (2020) 055001, https://doi.org/10.1088/1361-6404/ab9930
A.D. Fokker, The rising top, experimental evidence and theory, Physica 8 (1941) 591, https://doi.org/10.1016/S0031-8914(41)80039-1
D.G. Parkyn, The rising of tops with rounded pegs, Physica 24 (1958) 313, https://doi.org/10.1016/S0031-8914(58)95049-3
E.J. Routh, Advanced Dynamics of a System of Rigid Bodies, (Dover, New York, 1955), pp. 143-144, 192-194
J.H. Jellett, A treatise on the theory of friction, (Hodges, Foster and co., Dublin, 1872), pp. 181-187
T. Yogi, A Motion of Top by Numerical Calculation, J. Phys. Soc. Jpn. 73 (2004) 2093, https://doi.org/10.1143/JPSJ.73.2093
A. Gray, A Treatise on Gyrostatics and Rotational Motion, (Macmillan, London, 1918), p. 393
J. Perry, Spinning tops, (Society for Promoting Christian Knowledge, London, 1890), pp. 68-73
N.M. Hugenholtz, On tops rising by friction, Physica 18 (1952) 515, https://doi.org/10.1016/S0031-8914(52)80052-7
C.M. Braams, On the influence of friction on the motion of a top, Physica 18 (1952) 503, https://doi.org/10.1016/S0031-8914(52)80051-5
H.K. Moffatt, Y. Shimomura and M. Branicki, Dynamics of an axisymmetric body spinning on a horizontal surface. I. Stability and the gyroscopic approximation, Proc. R. Soc. Lond. A 460 (2004) 3643, https://doi.org/10.1098/rspa.2004.1329
R. Cross, The rise and fall of spinning tops, Am. J. Phys. 81 (2013) 280, https://doi.org/10.1119/1.4776195
T.J. Quinn and A. Picard, The mass of spinning rotors: no dependence on speed or sense of rotation, Nature 343 (1990) 732, https://doi.org/10.1038/343732a0
J.D. Anderson, Fundamentals of Aerodynamics, 2nd ed. (McGraw-Hill Companies, New York, 1984), pp. 54-66
V. Tanrıverdi, Can a gyroscope reverse its spin direction?, Eur. J. Phys. 40 (2019) 065004, https://doi.org/10.1088/1361-6404/ab335d
V. Tanrıverdi, Motion of the Gyroscope With Equal Conserved Angular Momenta, Eur. J. Phys. 41 (2020) 025004, https://doi.org/10.1088/1361-6404/ab6415
F. Klein and A. Sommerfeld, The theory of the Top, Volume II, (Birkhauser, New York, 2010), pp. 247
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